The length of wire is 82.78 foot.
After guiding wire,
It form a right angle triangle which have
One angle is of 65 degree
perpendicular = 75 foot
And we have to find hypotenuse of the triangle which is length of wire.
Since we know that,
The trigonometric ratio sin is the ratio of opposite side of angle and
hypotenuse.
Therefore,
⇒ Sin65 = 75/hypotenuse
⇒ 0.906 = 75/hypotenuse
⇒ hypotenuse = 82.7 foot
Since hypotenuse of triangle represents length of wire
So, required length of wire is 82.7 foot.
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The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.6 ppm and standard deviation 1.3 ppm. 15 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.a-What is the distribution of X? X ~ N(........,.......) b-What is the distribution of X bar? X bar ~ N(......,.....) c-What is the probability that one randomly selected city's waterway will have less than 9.3 ppm pollutants?
d-For the 15 cities, find the probability that the average amount of pollutants is less than 9.3 ppm.
e)For part d), is the assumption that the distribution is normal necessary? yes or no f. Find the IQR for the average of 15 cities.
Q1 = ............ ounces
Q3 = ............ ounces
IQR: ............ ounces
The interquartile range for the average of 15 cities is 1.8.
a) X ~ N(9.6, 1.3)
b) X bar ~ N(9.6, 0.13)
c) The probability that one randomly selected city's waterway will have less than 9.3 ppm pollutants can be calculated using the z-score formula: P(X < 9.3) = P(Z < (9.3 - 9.6) / 1.3) = 0.338.
d) The probability that the average amount of pollutants is less than 9.3 can be calculated using the z-score formula: P(Xbar < 9.3) = P(Z < (9.3 - 9.6) / 0.13) = 0.819.
e) The assumption that the distribution is normal is indeed necessary for part d.
f) The IQR for the average of 15 cities can be calculated as follows: Q1 = 8.7 and Q3 = 10.5. IQR = 10.5 - 8.7 = 1.8.
Therefore, the interquartile range for the average of 15 cities is 1.8.
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Solve this question briefly If you can
The solution of the equation, | x + 10 / 2x + 1 | = 20 is x = 10 / 39 or x = -30 / 41.
How to solve absolute equation?The absolute equation can be solved as follows:
| x + 10 / 2x + 1 | = 20
Therefore,
x + 10 / 2x + 1 = 20 or x + 10 / 2x + 1 = - 20
cross multiply
x + 10 / 2x + 1 = 20
x + 10 = 20(2x + 1)
x + 10 = 40x + 20
x - 40x = 20 - 10
-39x = -10
x = 10 / 39
x + 10 / 2x + 1 = - 20
cross multiply
x + 10 = -20(2x + 1)
x + 10 = -40x - 20
x + 40x = -20 - 10
41x = -30
divide both sides of the equation by 41
x = - 30 / 41
Therefore, x = 10 / 39 or x = -30 / 41
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You want to take out a $219,000 mortgage (home loan). The interest rate on the loan is 4.5%, and the loan is for 30 years. Your monthly payments are $1,109.64. How much will still be owed after making payments for 15 years? Round your answer to the nearest dollar.
After making payments for 15 years, the amount still owed on the mortgage would be approximately $145052.36.
To determine how much will still be owed after making payments for 15 years, we can use the formula for the remaining balance on a mortgage:
Remaining balance = P ((1 + r)ⁿ - (1 + r)ᵇ) / ((1 + r)ⁿ - 1)
where:
P = the initial loan amount (in this case, $219,000)
r = the monthly interest rate (which is the annual interest rate divided by 12)
n = the total number of monthly payments (which is 30 years times 12 months per year, or 360 months)
b = the number of monthly payments made so far (which is 15 years times 12 months per year, or 180 months)
First, we need to calculate the monthly interest rate:
r = 4.5% / 12 = 0.00375 = 0.375%
Next, we can plug in the values to get:
Remaining balance = $219,000 ((1 + 0.00375)³⁶⁰- (1 + 0.00375)¹⁸⁰) / ((1 + 0.00375)³⁶⁰ - 1)
= $145052.36
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Express using summation notation: 1^2+2^2+3^2+…+750^2
Answer:
⟶ We can express the sum 1^2 + 2^2 + 3^2 + ... + 750^2 using summation notation as:
∑i^2, where i goes from 1 to 750.
⟶ Here, the symbol ∑ represents the summation, and i is the index variable, which takes on the values 1, 2, 3, ..., 750. The expression i^2 is the term being summed.
⟶ So the sum can be written as:
∑i^2 = 1^2 + 2^2 + 3^2 + ... + 750^2
⟶ Note that the upper limit of the index variable is 750, which corresponds to the last term in the sum.
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Answer:
[tex]\sum \limits^{750}_{n=1} {n^2}[/tex]
Step-by-step explanation:
General explanation of summation notation
Any sum of terms whose format is the same can be represented more concisely using a Summation symbol.
The Summation symbol is a capital greek letter Sigma: [tex]\sum[/tex]
The summation will take a general format of each term, and increase a "dummy variable" by 1, summing together terms until the summation is complete. To write the summation expression, find the common format of each term, and write it using a "dummy variable" to represent the number that is changing.
If the change of the number within each term increases by 1 each time, that makes the transition easier because the dummy variable increases by 1. If the change of the number within each term does not change by 1 each time, using summation notation can be more challenging, as one needs to develop a formula to represent the amount that it is changing each time.
The common format of each term & the changing number
In our case, each term is some number squared, and the number that is squared changes from 1, to 2, to 3, ... and so on .. up to 750 (changing by 1 each time). Since the number that is square changes by 1 each time, that will be our "dummy variable".
Using "n" for the "dummy variable", our terms look like [tex]n^2[/tex]
The start and end of the list
Lastly, to specify where the list starts and ends, we write where the list starts (lowest number) at the bottom with the "dummy variable", and where the list ends (largest number) at the top.
So, in the end, the summation would look like this: [tex]\sum \limits^{750}_{n=1} {n^2}[/tex]
This represents adding a bunch of terms that look like [tex]n^2[/tex], starting at n=1, each time, increasing the value of n by 1, and stopping with the last term when n=750.
Extension of knowledge (NOT about THIS problem)
For a similar example where the changing number doesn't increase by 1 each time, look at a similar sequence of, where it's just the odd numbers squared up to 99:
1^2 + 3^2 + 5^2 + … + 99^2
While the terms do have the format of a number squared, since the number that is squared isn't just increasing by 1 each time, there would need to be a formula to describe how they are increasing. One way to represent that would be:
[tex]\sum \limits^{50}_{n=1} {(2n-1)^2}[/tex]
Note that this does cause the final endpoint of the dummy variable to not necessarily be intuitive, but the "99 squared" is the 50th term (observe 2*50-1 is 99).
7. Your ability to borrow money at lower rates improves as you save more ○ you earn more O your debt ratio increases your credit score increases ____. (1 point)
Answer:True
Lower interest rates reuslt in saving more money.
Figure Y is the result of a transformation on Figure X. Which transformation would accomplish this?
A. a reflection over the x -axis
B. a rotation 90° clockwise about the origin
C. a rotation 180° counterclockwise about the origin
D. a translation 10 units to the left and 10 units down
A transformation would accomplish this include the following: C. a rotation 180° counterclockwise about the origin.
What is a rotation?In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).
Furthermore, the mapping rule for the rotation of a geometric figure 180° counterclockwise about the origin is given by this mathematical expression:
(x, y) → (-x, -y)
Coordinates of point X (0, 4) → Coordinates of point Y = (0, -4)
Coordinates of point X (1, 3) → Coordinates of point Y = (-1, -3)
In conclusion, we can logically deduce that this transformation rule (x, y) → (-x, -y) would map Figure X onto Figure Y.
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Question 6
Sharron gets a total of £1050 each month.
She spends 3/10 of this on rent and 2/3 on food and bills.
How much money does Sharron have remaining?
Show your working out and write your answer in the box below.
Here are two triangles show that the triangles are similar what is the scale factor from triangle abc to abc
The two triangles are similar because angle C = C' and angle A = A'. The scale factor is 4/3
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. The corresponding angles of similar triangles are congruent.
Also, the ratio of corresponding sides of similar triangles are equal.
Therefore to show that that the two triangles are equal;
Tan A = 4/3
Tan A = 1.333
A = 53.1°
Tan A' = 5.3/4
Tan A' = 1.33
A' = 53.1°
Therefore the two triangles are similar.
The scale factor = 4/3
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help with number 6 please
The diameter of the second pile of phosphate is found to be approximately 62.6 feet.
The volume of a right circular cone is given by the formula,
V = (1/3)πr²h where volume is V, radius of the base is r, height is h, and π is approximately 3.14159. For the first pile of phosphate,
h = 15.3 feet
d = 48.6 feet
r = d/2 = 24.3 feet
Using the formula for the volume of a cone,
V = (1/3)πr²h
V = (1/3)π(24.3)²(15.3)
V = 24,249.8 cubic feet
For the second pile of phosphate,
h = 15.3 - 3.6 = 11.7 feet
r = ? (to be determined)
Using the same formula for the volume of a cone,
V = (1/3)πr²h
V = (1/3)πr²(11.7)
Since the volume of both piles is the same, we can set the two volume formulas equal to each other,
(1/3)π(24.3)²(15.3) = (1/3)πr²(11.7)
Simplifying,
(24.3)²(15.3) = r²(11.7)
r² = (24.3)²(15.3)/11.7
r = 31.3 feet (rounded to the nearest tenth)
Therefore, the diameter of the second pile of phosphate is d = 2r = 62.6 feet (rounded to the nearest tenth).
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Complete question - As phosphate is mined, it moves along a conveyor belt, falling off of the end of the belt into the shape of a right circular cone, as shown.
Height of the cone is 15.3 feet
Diameter of the base of cone is 48.6 feet
A shorter conveyor belt also has phosphate falling off of the end into the shape of a right circular cone. The height of the second pile of phosphate is 3.6 feet shorter than the height of the first. The volume of both piles is the same. To the nearest tenth of a foot, what is the diameter of the second pile of phosphate?
If a town's population doubles every 4 years, how
many people will be in the down 12 years later if the
current population is 28,100? y = ab*
The population of the town 12 years later will be 224,800 if the current population is 28,100 and the population doubles every 4 years.
Since the population doubles every 4 years, we can use the formula:
P = P0 x [tex]2^{t/4}[/tex]
where P0 is the initial population, t is the time elapsed in years, and P is the population after time t.
In this case, the initial population P0 is 28,100, and we want to know the population after 12 years, so t = 12. Substituting these values into the formula, we get:
P = 28,100 2^(12/4)
= 28,100 x 2³
= 28,100 * 8 = 224,800
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Ordena las siguientes medidas de mayor a menor. 5 dam³ 530 m³ 5.480 m³ 5,5 dam 5 dam 61 m²
The set of capacity measures related to cubic meter are ordered from the greatest to the least:
5.5 dam³, 5.480 m³, 5 dam³, 5 dam³, 530 m³, 61 m³
How to order different capacity measures
In this problem we need to order a group of capacity measures in cubic meters and its related units from the greateast to the least. To make this we need to understand the following relations:
1 dam³ = 1000 m³1 m³ = 1 m³Now we proceed to order the following set of information:
First, write the set of measures:
5 dam³, 530 m³, 5.480 m³, 5.5 dam³, 5 dam³, 61 m³
Second, convert all measures in cubic decameters into cubic meters:
5.000 m³, 530 m³, 5.480 m³, 5.500 m³, 5.000 m³, 61 m³
Third, order all the set from the greatest to the least:
5.500 m³, 5.480 m³, 5.000 m³, 5.000 m³, 530 m³, 61 m³
Fourth, rewrite the set of measures in its original units:
5.5 dam³, 5.480 m³, 5 dam³, 5 dam³, 530 m³, 61 m³
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PLEASE HELP ME
Which of these triangles are definitely right triangles?
(Note that not all triangles are drawn to scale.)
(Select all that apply.)
A
B
C
D
E
Answer:
I'd like to explain more but I have limited comment
chat me up
A
What is the area of this figure? 4 ft 13 ft 4 ft 4 ft 13 ft 9 ft 8 ft 4 ft 24 ft 7 ft 5 ft 15 ft Write your answer using decimals, if necessary.
The area of the figure is 183.5 ft².
We have,
The figure has two types of shapes.
Two rectangles and one triangle.
Now,
Area of rectangle = Length x Width
Area of triangle = 1/2 x base x height
Now,
Rectangle 1:
Area = 7 x 5 = 35 ft²
Rectangle 2:
Area = 4 x (4 + 5) = 4 x 9 = 36 ft²
Triangle:
Area = 1/2 x (11 + 4) x 15 = 1/2 x 15 x 15 = 112.5 ft²
Now,
The area of the figure.
= 35 + 36 + 112.5
= 183.5 ft²
Thus,
The area of the figure is 183.5 ft².
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in triangle QRS, the measure of angle RSQ is 48.2 degrees, and the SQR is 75 degrees. what is the QRS?
The measure of angle QRS in triangle QRS is 56.8 degrees.
To find the measure of angle QRS in triangle QRS, we can use the fact that the sum of the measures of the angles in a triangle is always 180 degrees.
We know that:
- The measure of angle RSQ is 48.2 degrees
- The measure of angle SQR is 75 degrees
Let x be the measure of angle QRS. Then, we can write:
RSQ + SQR + QRS = 180
Substituting the known values, we get:
48.2 + 75 + x = 180
Simplifying and solving for x, we get:
x = 180 - 48.2 - 75x = 56.8
Therefore, the measure of angle QRS in triangle QRS is 56.8 degrees.
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Food fryers manufactured by a company that supplies food trucks can fry a mean of 132.4 pounds of food per hour with a standard deviation of 3.9 pounds per hour. In a given hour, how much food would 95% of these fryers fry?
I need more help please!!!
Answer:
Hi!, if you need help right away, chat with a tutor!
Step-by-step explanation:
The diameter of a circle is 8cm. Find its circumference to the nearest tenth.
Answer:
[tex]C = 25.1 \text{ cm}[/tex]
Step-by-step explanation:
We can find the circumference of the circle by plugging the given radius value 8 cm into the formula:
[tex]C = \pi d[/tex]
Note: This formula can also be written as [tex]C = 2\pi r[/tex] because [tex]2r = d[/tex].
↓ plugging in the given radius
[tex]C = 8\pi \text{ cm}[/tex]
↓ rounding to the nearest tenth
[tex]\boxed{C = 25.1 \text{ cm}}[/tex]
WILL GIVE BRAINLIEST PLEASE HELP!
Question 10
The reason that Rachel could give for her proof is given as follows:
<1 ≅ <5 by the Corresponding Angle Theorem.
What are corresponding angles?When two parallel lines are cut by a transversal, corresponding angles are pairs of angles that are in the same position relative to the two parallel lines and the transversal.
Corresponding angles are always congruent, which means that they have the same measure.
A pair of corresponding angles in this problem is given as follows:
<1 and <5.
Hence they are congruent. <8 is opposite by the same vertex with <5, hence they are also congruent, and by the transitive property of congruence, we have that:
<8 ≅ <1, as <8 ≅ <5 and <5 ≅ <1.
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−9, −4, 1, 6, .. aremetric or geometric
please helpppp!!!
You are a male who just graduated from college with a bachelor's degree. You have a job paying $50,780.00/yr.
a.How does your salary compare to the yearly median earnings for a male with a bachelor's degree?
b. What is the difference between the yearly median earnings for a male with a bachelor's degree compared to a male who does not attend college after earning a high school diploma?
The salary $50,780 per year is lower than the yearly median.
The yearly median earnings for a male with a bachelor's degree are $40,404 higher than those for a male with a high school diploma.
a. As, the median weekly earnings for males with a bachelor's degree are $1,384.
To convert this to yearly earnings, we can multiply by the number of weeks in a year (52):
= $1,384 x 52
= $71,968
So, the salary $50,780 per year is lower than the yearly median earnings for a male with a bachelor's degree.
b. Now, The yearly median earnings for a male with a high school diploma (no college) are $607 per week. Converting this to yearly earnings:
Yearly median earnings for a male with a high school diploma
= $607 x 52 = $31,564
The difference between the yearly median earnings for a male with a bachelor's degree and a male with a high school diploma is:
= $71,968 - $31,564 = $40,404
So, the yearly median earnings for a male with a bachelor's degree are $40,404 higher than those for a male with a high school diploma.
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Determine which conic section is represented based on the given equation: 4x^2+9xy+4y^2-36y-125=0
The conic section of the equation 4x² + 9x +4y² - 36y - 125 = 0 is a circle
Selecting the conic section of the equationThe given equation is
4x² + 9xy + 4y² - 36y - 125 =0
The above equation is an illustration of a circle equation
The standard form of a circle equation is
(x - a)² + (y - b)² = r²
Where
(a, b) is the center
r is the radius
While the general form of the equation is
ax² + fx + by² + gy + c =0
Where c is a constant
Recall that, we have
4x² + 9x + 4y² - 36y - 125 =0
This is the general form
We can convert to the standard form as follows
Divide through by 4
x² + 2.25x + y² - 9y - 31.25 =0
Next, we complete the square of the x-terms and the y-terms
For the x-terms, we have
x² + 2.25x = x² + 2.25x + (2.25/2)² - (2.25/2)²
x² + 2.25x = (x + 2.25/2)² - (2.25/2)²
For the y-terms, we have
y² - 9y = y² - 9y + (9/2)² - (9/2)²
y² - 9y = (y - 9/2)² - (9/2)²
Substitute the new x and y terms
So, x² + 2.25x + y² - 9y - 31.25 = 0 becomes
(x + 2.25/2)² - (2.25/2)² + (y - 9/2)² - (9/2)²- 31.25 =0
Evaluate the sum of like terms
(x + 2.25/2)² + (y - 9/2)² - 3377/64 = 0
So, we have
(x + 9/8)² + (y - 9/2)² = 3377/64
Using the above as a guide, we can conclude that the conic section of the equation is a circle
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Haley is returning from a business trip. Her empty suitcase has a mass of 5.1 kg. Her clothes have a combined mass of 14.8 kg. Haley also wants to pack 4 gifts, each with a mass of 870 g. The airline restriction for a suitcase is a limit of 22.7 kg. Can Haley bring everything home in her suitcase? If not, how many gifts can she pack? Explain.
From the calculation, she can't carry all but she can carry her suitcase with clothes in it and three out of the four gift items.
What can she pack?We know that we have to consider the restriction that the airline has placed. We have been told that the luggage that have to be packed in this case would have to be less than 22.7 kg.
We would now have to look at all the things that Haley would need to pack so as to determine what can be packed and what can not be packed.
Total luggage that she has to pack;
Mass of empty suitcase + mass of her clothes + mass of 4 gifts
Total luggage = 5.1 Kg + 14.8 Kg + 4(0.87) = 23.38 Kg
This implies that she can't carry all but she can carry her suitcase with clothes in it and three out of the four gift items.
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.will give brainless
Step-by-step explanation:
OK, 'Brainless'.... the triangle side length rule states that any two sides of a triangle must sum to greater than the remaining side length...
42 + 20 > x then 12 , 20, 22, 32, 42, 50 will work here
42+x > 20 all of the possibles work here
20 + x > 42 32, 42, 50, 62 and 70 work here
so 32 and 42 are in all of the lists ....that is your answer
(20 points) I really need help with this problem, if someone who 100% knows the answer and can show step by step. please and thank you!
The total surface area of the given pyramid is: 95 ft²
What is the surface area of the pyramid?To get the surface area of the given pyramid, we will find the individual areas of all surfaces and add up to get the total surface area.
Formula for area of a triangle is:
A = ¹/₂bh
where:
b is base
h is height
Formula for area of a rectangle is:
A = Length * Width
Thus:
Total surface area of pyramid = 4(¹/₂ * 5 * 7) + (5 * 5)
Total surface area of pyramid = 70 + 25
Total surface area of pyramid = 95 ft²
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Five runners need to be arranged in 5 lanes for a race so that there is a runner in each lane
How many unique ways are there to arrange the numbers in the 5 lanes
Step-by-step explanation:
5 P 5 = 120 ways = 5!
Pls hep!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
98 mm²
Step-by-step explanation:
This parallelogram has a base of 7 and height of 14 mm.
The height is the vertical distance between the two bases
The area = b x h = 7 x 14 = 98 mm²
[tex]\huge\mathcal{\fcolorbox{aqua}{azure}{\red{➳Aɳʂɯҽɾ}}}[/tex]
Refer the attachment for clarity:-
[tex] \colorbox{yellow}{\red{Formula\: Base\: x \:Height= Area}}[/tex]
[tex]\sf{\leadsto 7×14}[/tex]
[tex]{ \red{ \sf 98m {m}^{2} }}[/tex]
______________________________
[tex]\bold{Thank ~you~:)}[/tex]
End Behavior
Describe the end behavior of the following functions using limit notation, please.
1. f(x) = (2x² + 4x + 4) / x³ = 0; as lim x→∞, and lim x→-∞
2. g(x) = (2x² + 4x + 4)/x² = ∞; as lim x→∞, and lim x→-∞]
3. h(x) = (2x² + 4x + 4)/x = ∞ as lim x→∞, and -∞ as lim x→-∞.
What is the behavior of the functions?To find the end behavior of each of the functions, we can take the limit as x approaches infinity and negative infinity.
For f(x) = (2x² + 4x + 4)/x³;
lim x→∞ (2x² + 4x + 4) / x³ = 0
lim x→-∞ (2x² + 4x + 4) / x³ = 0
f(x) approaches zero as x approaches positive or negative infinity.
For g(x) = (2x² + 4x + 4)/x²;
lim x→∞ (2x² + 4x + 4) / x² = ∞
lim x→-∞ (2x² + 4x + 4) / x² = ∞
g(x) approaches infinity as x approaches positive or negative infinity.
For h(x) = (2x² + 4x + 4)/x
lim x→∞ (2x² + 4x + 4) / x = ∞
lim x→-∞ (2x² + 4x + 4) / x = -∞
h(x) approaches infinity as x approaches positive infinity, and negative infinity as well, but with a negative sign.
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Alice is cutting pieces of cloth to sew into a quilt. She cut one piece of cloth into a parallelogram with a base of 7 inches and a height of 4 inches. What is the area of this piece of cloth?
Answer:
28 in²
Step-by-step explanation:
Area of parallelogram = base X vertical height
= 7 X 4
= 28 in²
I need the answer to the problem
Asher solved the equation below:
4x = 64
4x − 4 = 64 − 4
x = 60
Is Asher's solution correct? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation.
your wrong you divide by 4 60/4=15 there